HP 50g Graphing Calculator User Manual

Page 508

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Page 16-31

The result is c

n

= (i

⋅n⋅π+2)/(n

2

⋅π

2

).

Putting together the complex Fourier series
Having determined the general expression for c

n

, we can put together a finite

complex Fourier series by using the summation function (

Σ) in the calculator as

follows:

Θ First, define a function c(n) representing the general term c

n

in the complex

Fourier series.

Θ Next, define the finite complex Fourier series, F(X,k), where X is the

independent variable and k determines the number of terms to be used.
Ideally we would like to write this finite complex Fourier series as

However, because the function c(n) is not defined for n = 0, we will be
better advised to re-write the expression as

)

2

exp(

)

(

)

,

(

X

T

n

i

n

c

k

X

F

k

k

n

=

=

π

+

= 0

)

0

,

,

(

c

c

k

X

F

)],

2

exp(

)

(

)

2

exp(

)

(

[

1

X

T

n

i

n

c

X

T

n

i

n

c

k

n

+

=

π

π

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